Here's the funky DNS dance:
0) Pick a domain to test with
1) Set up the new DNS box to be primary for it
2) Make the old primary a slave of the new one (temporarily)
3) Make the old secondary also a slave of the new primary (temporarily)
4) Get our ISP sussed to provide secondary and tertiary DNS post-switchover
5) HUP all the nameds :-)
6) Get the domain NS records for the test domain swapped from the old primary and secondary to the new primary, secondary and tertiary addresses
7) Once propagated 'round the net, remove the domain from the old primary and secondary
... then repeat for the other 196 domains, and after that I can start on the mail migration project.
Once that's done, then I might be able to finally decommission the old primary DNS/Mail machine - whoopee!